https://file.aiquickdraw.com/mathbot/file/1728280643956zuklqp5i.jpg

Let's solve the multiplication problem: \((5x + 9)(3x + 1)\).

We will expand the expression using the distributive property (also known as the FOIL method for binomials):

1. **First**: \(5x \cdot 3x = 15x^2\)
2. **Outer**: \(5x \cdot 1 = 5x\)
3. **Inner**: \(9 \cdot 3x = 27x\)
4. **Last**: \(9 \cdot 1 = 9\)

Now, we add all these terms together:
\[
15x^2 + 5x + 27x + 9
\]

Combine the like terms:
\[
15x^2 + 32x + 9
\]

So, the final expression is:
\[
(5x + 9)(3x + 1) = 15x^2 + 32x + 9
\]

You can now fill in the blanks as:
- First box: \(15\)
- Second box: \(32\)
- Third box: \(9\)

Would you like more details on any part of the process?

Here are 5 related questions you can try:
1. How do you apply the distributive property to binomials?
2. What happens when both terms in a binomial have negative coefficients?
3. How do you multiply polynomials with more than two terms?
4. What is the difference between expanding and factoring expressions?
5. Can you simplify the expression \((7x - 5)(2x + 3)\)?

**Tip**: Always combine like terms after expanding, as this simplifies your expression.

Learn how to multiply the binomials (5x + 9)(3x + 1) using the distributive property. This problem helps reinforce key algebraic concepts such as binomial expansion and polynomial multiplication. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation